I'm the Scrum Master on a cross-functional team that initially had little to no experience with Agile. I think Barnaby's answer is great and definitely something to strive for. From what I've observed, though, if the team doesn't have a certain level of maturity (Agile-wise), they won't necessarily learn if you leave them to their own devices. If in their career, a team member has never had the space to take initiative, they won't naturally decide to do that when you leave them space. Teams need to define what self-organization mean from them, but providing some structure and nudging them in the "right" direction goes a long way, especially early on in the process. It's always hard to figure out what the right balance of guidance vs. freedom is to get the team to a point where they're a model of self-organization, but I think Mike Cohn's Situational Scrum Mastering explains this well.
I've encountered all of the issues you've mentioned, and the two things that I've found work well to address them are:
1) Using retrospectives as an opportunity for team members to become aware of those issues. Ideally, wait for them to flag them, but if they don't have that reflex yet and you think they're missing the boat, come up with a set of questions that will lead them in that direction. You can even dedicate the whole retro to a single topic if you feel it'd be helpful.
2) Showing short (5- to 10-minute) videos related to agile principles and values and facilitating a discussion afterwards. In the last few months, I've been dedicating 15 minutes to that in our weekly meetings, and it's worked wonders. I've noticed team members referencing concepts they've seen in the videos, and slowly but surely applying them in their work. I've found the Scrum Life series to be particularly helpful in that regard (slow down the pace and use English subtitles if necessary).